Designed a novel implementation of a method that forecasts asset covariances (particularly volatility) using daily candlestick price data and tested it using a portfolio optimzation problem composed of multi-asset futures of SP500, US 10-Year Treasuries, Gold, and WTI Crude Oil.
ARCH and GARCH type models: Diagonal BEKK, Orthogonal GARCH, Constant Conditional Covariance (CCC), GARCH-Dynamic Conditional Covariance
MA type models: EWMA
Others: Heterogneous Autoregressive (HAR) and HAR DRD , Hybrid Implied Covariance, Random Walk Estimator
\[\sigma_{i,t+1}^{(d)} = c + \beta^{(d)}RV_{i,t}^{(d)} + \beta^{(w)}RV_{i,t}^{(w)} + \beta^{(m)}RV_{i,t}^{(m)} + \epsilon_{i,t+1}^{(d)},\] \[ i = 1,2,3,4 \]
Where,
\[ RV_{i,t}^{(d)} = \sqrt{\frac{1}{N}\sum_{k=1}^N r_{k,t}^2} \] \[RV_{i,t}^{(w)} = \frac{1}{5} \sum_{k=0}^4 RV_{i,t-k}^{(d)} \] \[RV_{i,t}^{(m)} = \frac{1}{21} \sum_{k=0}^{20} RV_{i,t-k}^{(d)} \]
\[vech(R_{t+1}) = vech(\bar{R}_T)(1 - \alpha - \beta - \gamma) + \alpha\cdot vech(R_{t}) + \beta\cdot vech(R_{t-4:t}) + \gamma\cdot vech(R_{t-20:t})+ vech(\epsilon_{t+1})\]
HAR models typically are implemented using high frequency intraday returns data which are expensive to obtain, computationally challenging to work with, and often exhibit significant noise.
Intraday returns are subject to market microstructure effects, which results in measurement errors when using them in daily volatility and correlation estimates.
Sum of average squared returns as a variance estimator assumes zero drift.
Daily log range: \(\ln(\frac{High}{Low})\)
Parkinson’s variance: \(\frac{(\ln(\frac{High}{Low}))^2}{4\ln 2}\)
While far less noisy and requiring lesser data, these estimators also assume zero drift which is not always the case.
Introduced an alternative estimator for daily realized volatility developed by Rogers and Satchell (1991):
\[ RV_{i,t}^{(d)} = \sqrt{u_{i,t}(u_{i,t} - c_{i,t}) + d_{i,t}(d_{i,t} - c_{i,t})},\] \[u_{i,t} = \ln H_{i,t} - \ln O{i,t}\] \[d_{i,t} = \ln L_{i,t} - \ln O{i,t}\] \[c_{i,t} = \ln C_{i,t} - \ln O{i,t},\] \[ i = 1,2,3,4 \]
Unlike volatility, we cannot estimate intraday correlation using just candlestick data because temporal information is lost.
To maintain daily portfolio rebalancing while smoothening correlations, we propose to rolling weekly correlations. On each day, the correlation forecast would be over the following week.
\[vech(R_{t+1:t+5}) = vech(\bar{R}_T)(1 - \alpha - \beta) + \alpha\cdot vech(R_{t-4:t}) + \beta\cdot vech(R_{t-20:t}) + vech(\epsilon_{t+1:t+5})\]
Using data between 2002-2017 to train the model:
Coefficients for the volatility regression are more significant as the time horizon increases, exhibiting the long memory and persistance behavior of volatility. Correlations also show a similar property.
Generated forecast errors by measuring Euclidean distance \((L_2\) norm) between forecasted and actual vectorized volatility and correlation matrices, respectively, observed during 2018-2022.
\[ Min \,\, \omega^T \Sigma \omega \] \[ s.t.: \,\,\sum_{i=1}^n \omega_i = 1,\,\omega_i \ge 0, \forall_i,\]
where \(\omega\) is the vector of portfolio weights and \(\Sigma\) is the covariance matrix of asset returns.
Immediate improvements to the project can be made:
Other future innovations can include:
suran021@umn.edu